Quadratic Equations Practice
Get zero on one side, then factor, take square roots, or use the quadratic formula.
Last updated
Solve for x.
12 problems
- 1.
- 2.x² − 225 = 0Answerx=15, x=−15
Move −225 to the other side
x²=225Take the square root of both sides
x=15, x=−15
- 3.(x + 2)(x − 2) = 0Answerx=−2, x=2
Split into cases
x+2=0, x−2=0Move 2 to the other side
x=−2, x−2=0Move −2 to the other side
x=−2, x=2
- 4.(x + 6)(x − 6) = 0Answerx=−6, x=6
Split into cases
x+6=0, x−6=0Move 6 to the other side
x=−6, x−6=0Move −6 to the other side
x=−6, x=6
- 5.x² − 14x = 0Answerx=14, x=0
Factor
(x−14)×x=0Split into cases
x−14=0, x=0Move −14 to the other side
x=14, x=0
- 6.(x − 3)² = 16Answerx=7, x=−1
Take the square root of both sides
x−3=4, x−3=−4Move −3 to the other side
x=7, x−3=−4Move −3 to the other side
x=7, x=−1
- 7.(x + 9)² = 25Answerx=−4, x=−14
Take the square root of both sides
x+9=5, x+9=−5Move 9 to the other side
x=−4, x+9=−5Move 9 to the other side
x=−4, x=−14
- 8.x² + 6x + 8 = 0Answerx=−2, x=−4
Factor
(x+2)×(x+4)=0Split into cases
x+2=0, x+4=0Move 2 to the other side
x=−2, x+4=0Move 4 to the other side
x=−2, x=−4
- 9.x² − 6x + 8 = 0Answerx=4, x=2
Factor
(x−4)×(x−2)=0Split into cases
x−4=0, x−2=0Move −4 to the other side
x=4, x−2=0Move −2 to the other side
x=4, x=2
- 10.x² − 8x + 16 = 0Answerx=4, x=4
Factor
(x−4)²=0Take the square root of both sides
x−4=0, x−4=0Move −4 to the other side
x=4, x−4=0Move −4 to the other side
x=4, x=4
- 11.x² − 5x = 14Answerx=7, x=−2
Move 14 to the other side
x²−5×x−14=0Factor
(x−7)×(x+2)=0Split into cases
x−7=0, x+2=0Move −7 to the other side
x=7, x+2=0Move 2 to the other side
x=7, x=−2
- 12.x² + 7x + 7 = 0Answerx=−7/2+1/2×√(21), x=−7/2−1/2×√(21)
Use the quadratic formula
x=(−7±√(7²−4×1×7))/(2×1)Work out 7²
x=(−7±√(49−4×1×7))/(2×1)Work out 2×1
x=(−7±√(49−4×1×7))/2Split the fraction
x=−7/2±1/2×√(49−4×1×7)Work out −4×1×7
x=−7/2±1/2×√(49−28)Work out 49−28
x=−7/2±1/2×√(21)Split the ± into two cases
x=−7/2+1/2×√(21), x=−7/2−1/2×√(21)
Factoring is fastest when it works. x² = 100 needs only a square root: x = 10 or x = −10. The formula always works.
Common questions
- How many answers can a quadratic have?
- Two, one, or none among the real numbers.
- Which method should I use?
- Try factoring first. Use square roots when there is no x term, and the formula otherwise.
